engleski

A quadratic twist of the elliptic curve y^2 = x(x-1)(x-lambda)

In this paper we use a simple geometric idea to construct a family of quadratic twists g(u)y^2 = x(x − 1)(x − lambda) of rank at least two over Q(u), where g = g_lambda are suitable degree 7 polynomials over Q. The family does not fit in the examples coming from the method described in [8]. We make an extensive calculation which supports our belief that the rank is two for all  lambda in Q \ {; ; 0, 1}; ; .

elliptic curve; quadratic twist

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